We introduce a new methodology, which is based on the construction of epidemic networks, to analyse the evolution of epidemic time series. First, we translate the time series into ordinal patterns containing information about local fluctuations in disease prevalence. Each pattern is associated with a node of a network, whose (directed) connections arise from consecutive appearances in the series. The analysis of the network structure and the role of each pattern allows them to be classified according to the enhancement of entropy/complexity along the series, giving a different point of view about the evolution of a given disease.